The top U.S. military officer said Tuesday that American troops must be given immunity from prosecution as part of any agreement to keep them in Iraq beyond the end of the year and that this protection must be approved by Iraq’s parliament.

The comments by Joint Chiefs chairman Adm. Mike Mullen could make it more difficult for the troops to stay here.

Mullen and other U.S. officials have been pushing Iraq to decide whether they would want additional American forces to stay in the country past their Dec. 31 departure date, and the immunity issue has been one of the key sticking points.

“An agreement, which would include privileges and immunities for our American men and women in uniform will need to go through the COR,” said Mullen, referring to the Council of Representatives as Iraq’s parliament is known.

Washington has offered to let up to 10,000 U.S. troops stay and continue training Iraqi forces on tanks, fighter jets and other military equipment.